The midfielder has been sidelined for the club's last four matches after picking up the problem while on international duty with Belgium.
"We want to avoid surgery if we can," Villas-Boas told reporters. "If there happens to be surgery I think we are looking for one month, one month and a half.
"Hopefully that will not happen because we have some good indications the player will be back in one week or two weeks."
Dembele has scored one goal in nine appearances for Spurs following his summer move from Fulham.